Borel Ranks and Wadge Degrees of Omega Context Free Languages
Résumé
We show that, from a topological point of view, considering the Borel and the Wadge hierarchies, 1-counter Büchi automata have the same accepting power than Turing machines equipped with a Büchi acceptance condition. In particular, for each recursive non null ordinal alpha, there exist some Sigma^0_alpha-complete and some Pi^0_alpha-complete omega languages accepted by Büchi 1-counter automata.
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